Potential caused by masses of a homogeneous spheroid

By definition, the distance ri still obeys Equation (2.312) and, in accordance with Equations (2.313 and 2.329) 

The last integral is calculated using a new variable e cos 0 = t, and it gives 

the potential of the attraction field at any point inside the spheroid is 

We have demonstrated that as in the case of the spherical mass the attraction field increases linearly approaching the spheroid surface and it is equal to zero at the center. At the same time, the potential has a maximum at this point and then decreases gradually as a parabolic function and reaches a minimum on the surface of the spheroid. 

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